The stores are the only ones out of the chain of 21 Big W stores that have permission for food retailing, and they are to be split between the two supermarkets.
The out-of-town US-style concept stores were launched in the late 1990s but Woolworths is now reviewing its Big W format due to a lack of success in sales returns.
Asda has taken Big W stores in Aberdeen and Bolton and it in talks about one further outlet. It is believed to have paid up to £50m for one site, according to newspaper reports.
Tesco will buy the Big W outlet in Bedruth, Cornwall and is in final discussion about three more stores.